Paper
An automata-based test for bricks over string algebras
Authors
Amit Kuber, Annoy Sengupta
Abstract
Motivated by the recent work of Deaconu, Mousavand and Paquette on the connection between infinite string bricks for certain gentle algebras and Sturmian words, we develop a decorated version of a deterministic automaton, called a multi-entry inverse automaton (MIA, for short) that accepts pointed words. We then associate an MIA $\mathsf M_{Λδ}$ over $\{0,1\}$ to a string algebra $Λ$, and show that strings over $Λ$ can be viewed as certain equivalence classes of the pointed words accepted by $\mathsf M_{Λδ}$. By defining (weak) brick words over this MIA, we show that a finite/infinite string module (resp. band module) is a brick if and only if every word in the associated equivalence class of pointed binary words is a brick word (resp. a weak brick word) over $\mathsf M_{Λδ}$. The result of Deaconu et al. follows as an immediate consequence.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.18820v1</id>\n <title>An automata-based test for bricks over string algebras</title>\n <updated>2026-03-19T12:18:38Z</updated>\n <link href='https://arxiv.org/abs/2603.18820v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.18820v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Motivated by the recent work of Deaconu, Mousavand and Paquette on the connection between infinite string bricks for certain gentle algebras and Sturmian words, we develop a decorated version of a deterministic automaton, called a multi-entry inverse automaton (MIA, for short) that accepts pointed words. We then associate an MIA $\\mathsf M_{Λδ}$ over $\\{0,1\\}$ to a string algebra $Λ$, and show that strings over $Λ$ can be viewed as certain equivalence classes of the pointed words accepted by $\\mathsf M_{Λδ}$. By defining (weak) brick words over this MIA, we show that a finite/infinite string module (resp. band module) is a brick if and only if every word in the associated equivalence class of pointed binary words is a brick word (resp. a weak brick word) over $\\mathsf M_{Λδ}$. The result of Deaconu et al. follows as an immediate consequence.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.FL'/>\n <category scheme='http://arxiv.org/schemas/atom' term='math.RT'/>\n <published>2026-03-19T12:18:38Z</published>\n <arxiv:comment>11 pages, 4 figures</arxiv:comment>\n <arxiv:primary_category term='cs.FL'/>\n <author>\n <name>Amit Kuber</name>\n </author>\n <author>\n <name>Annoy Sengupta</name>\n </author>\n </entry>"
}